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Abby's utility function is given by U = X2Y2. For this utility function, MUx = 2XY2 and MUy = 2X2Y. If good X costs $10 and good Y costs $5, then Abby will consume ____ times as many units of good Y as she does units of good X.

a.1/2

b.2

c.4

d.3

Respuesta :

ogorwyne

Abby has to consume 2 times as many units Y as she does good X

The Utility function is given as

Utility = X²Y²

MUx = 2XY²

MUy = 2X²Y

The cost of good X = 10 dollars

The cost of good Y = 5$

At the optimum cost of consumption

[tex]\frac{MUx}{MUy} =\frac{X}{Y}[/tex]

[tex]\frac{2XY^{2} }{2X^{2}Y } = \frac{10}{5}[/tex]

When we cancel out the equation

[tex]\frac{Y}{X} = 2[/tex]

Y = 2X

In conclusion, Abby has to consume 2 times as many units Y as she does good X

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